Page 496 - Handbook of Properties of Textile and Technical Fibres

Tensile failure of polyester fibers 469

strength decrease due to the influence of environmental effects depends on the mech-
anism of degradation. There are three limit situations (Grassie and Scott, 1985):
1. The polymer chains randomly break but practically no volatile material is produced until late
in the degradation (random scission).
2. The decrease in molecular weight is proportional to the amount of volatile products and mol-
ecules that are volatile at the degradation conditions are progressively separated gradually
from the chain ends (depolymerization).
3. Whole polymer molecules disappear. This occurs most frequently when the polymer mole-
cule breaks to form macroradicals, which then depropagate to form monomers in a reaction
that is the exact reverse of the propagation process during polymerization.
In reality, the degradation usually lies between these extreme situations. There are
two main mechanisms of chain scission, i.e., depolymerization and random chain
scission. Depolymerization often occurs during thermal degradation. Random chain
scission is typical for hydrolytic degradation. In some situations, as in case of photo-
degradation, the chain scission mechanisms are combined with crosslinking (Grassie
and Scott, 1985). The rate of chain scission due to environmental breaking of ester
links in PET fibers increases with increasing of initial fiber carboxyl end-group con-
centration, i.e., with decreasing of molecular weight (Ravens and Ward, 1961).

13.4.2.1 Hydrolysis

The number of ester links initially in PET material with a degree of polymerization
DP ¼ M 0 /M n is equal to 2DP, where M 0 is the molecular weight of PET and
M m ¼ 192 is the weight of the PET monomer unit. In a PET chain there are initially
present N cg ¼ (DP 1) accessible ester links. After an environmental attack till
time t, there will be N cg N b ester links remaining where N b is equal to the number
of broken ester links at time t. The same weight of PET is now shared between
N b þ 1 pieces, so the number average molecular weight M t after time t is equal to
the M 0 /(N b þ 1) and N b ¼ M 0 /M t 1.
The rate of chain scission can be approximately expressed by the first-order reaction
relationship (Burgoyne and Merii, 2007):

dN b
¼ K s ðN cg N b Þ (13.30)
dt
where K s is the rate constant of chain scission. After integration, the number of broken
ester links due to chains scission can be obtained:

N b ¼ N cg ½1 expð K s tފ (13.31)

The corresponding number average molecular weight M t is then

M 0
M t ¼ (13.32)
1 þ N cg ½1 expð K s tފ